Iterated forcing with finitely additive measures: applications of probability to forcing theory
The method of finitely additive measures along finite support iterations was introduced by Saharon Shelah in 2000 (see [She00]) to show that, consistently, cov(N ) may have countable cofinality. In 2019, Jakob Kellner, Saharon Shelah and Anda Tanasie ˇ (see [KST19]) improved the method: they achieve...
- Autores:
-
Uribe Zapata, Andrés Felipe
- Tipo de recurso:
- Fecha de publicación:
- 2023
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/84529
- Palabra clave:
- 510 - Matemáticas
510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
510 - Matemáticas::511 - Principios generales de las matemáticas
Forcing (Teoría de los modelos)
Trayectoria aleatoria
Iterated forcing
Probability
Finitely additive measure
Consistency results
Null set
Intersection number
Cardinal invariant
Singular cardinal
Cichon’s diagram
Forcing iterado
Probabilidad
Medida finitamente aditiva
Resultados de consistencia
Conjunto nulo
Numero de intersección
Cardinal invariante
Cardinal singular
diagrama de Cicho´n
- Rights
- openAccess
- License
- Reconocimiento 4.0 Internacional
| Summary: | The method of finitely additive measures along finite support iterations was introduced by Saharon Shelah in 2000 (see [She00]) to show that, consistently, cov(N ) may have countable cofinality. In 2019, Jakob Kellner, Saharon Shelah and Anda Tanasie ˇ (see [KST19]) improved the method: they achieved some new generalizations and applications, such as separating the left side of Cichon’s ´ diagram with b < cov(N ). In this thesis, based on probability theory tools and the articles cited above, we develop a general theory of iterated forcing using finitely additive measures. For this purpose, we introduce two new notions: on the one hand, we define a new linkedness property, which we call “µ-FAM-linked” and, on the other hand, we generalize the notion of intersection number to forcing notions, which justifies the limit steps of our iteration theory. Finally, we apply our theory to prove in detail the consistency of cf(cov(N )) = ℵ0, and some separations of Cichon’s ´ diagram where cov(N ) is singular. In particular, we obtain a new constellation of Cichon’s diagram ´ separating the left side with cov(N ) singular |
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